Problem: N different natural numbers are given. If you select four different ones and set them as $ A $, $ B $, $ C $, $ D $, the following formula

$ \ Frac {A + B} {C --D} $



I want to find the maximum value of.




Given N different natural numbers, choose 4 different from them and create a program to find the maximum value of the above formula.



Input

The input is given in the following format.


N
a1 a2 ... aN


The number N (4 ≤ N ≤ 1000) of natural numbers is given in the first line. The value ai (1 ≤ ai ≤ 108) of each natural number is given in the second line. However, the same natural number does not appear more than once (ai ≠ aj for i ≠ j).

Output

Outputs the maximum value of the above formula as a real number for a given N natural numbers. However, the error must not exceed plus or minus 10-5.

Examples

Input

10
1 2 3 4 5 6 7 8 9 10


Output

19.00000


Input

5
22 100 42 3 86


Output

9.78947


Input

6
15 21 36 10 34 5


Output

18.00000


Input

4
100000 99999 8 1


Output

28571.285714

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
#define FOR(i,a,b) for (int i=(a);i<(b);i++)
#define RFOR(i,a,b) for (int i=(b)-1;i>=(a);i--)
#define REP(i,n) for (int i=0;i<(n);i++)
#define RREP(i,n) for (int i=(n)-1;i>=0;i--)
 
#define PB push_back
#define MP make_pair
#define ALL(a) (a).begin(),(a).end()
#define PII pair<int,int>
#define VS vector<string>
#define VI vector<int>
#define ll long long
#define ull unsigned long long
#define FST first
#define SEC second
int main(){
  int n;
  cin>>n;
  VI V(n);
  REP(i,n)cin>>V[i];
  sort(ALL(V));
  int mi=1e9;
  REP(i,n-3){
    mi=min(mi,V[i+1]-V[i]);
  }
  double ans=(double)(V[n-1]+V[n-2])/(double)mi;
  double d=(double)(V[n-3]+V[n-4])/(double)(V[n-1]-V[n-2]);
  ans=max(ans,d);
  d=(double)(V[n-1]+V[n-4])/(double)(V[n-2]-V[n-3]);
  ans=max(ans,d);
  printf("%.5f\n",ans);
  return 0;
}